Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22611720 | C2 | semidirect |
| 4. #22608036 | C2 | semidirect |
| 12. #17988369 | C4 | semidirect |
| 24. #14556531 | C2×C4 | semidirect |
| 149. C73 | #12923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611720 | 2 |
| C2×#17988369 | 2 |
| #22609964 | 2 |
| #22608036 | 2 |
| C73×#2911 | 2 |
| #12923 | 73 |